Synthetic estimators based on implicit linking models and their linear combinations with the direct estimators constitute an important subclass of the indirect estimators. They are considered in the traditional design-based estimation theory [1]}, where estimators of parameters are based only on the randomness induced by the sampling design. The composite estimation is the way to find a trade-off between large variances of the direct estimators and biases of the synthetic estimators. Even some modern indirect estimators, like the empirical best linear unbiased predictors (EBLUPs) [2]}, [3]}, built using linear mixed models, are expressed as the linear combinations of the direct and synthetic estimators. Explicit small area models, like those including random area-specific effects for EBLUPs, are a flexible tool in complex estimations. Therefore, these days they are considered superior to the traditional estimators. On the other hand, the latter design-based approach is desirable in sample surveys, and the estimators are pretty simple.
